I know that fight between Pikkon and Goku was filler in the anime, but Imagine SSJ2 Goku using Kaio Ken against Majin Vegeta
Kaio Ken is more of an ability than a transformation. And to be honest I don't think Goku can go kaio ken while SSJ outside of other world. Kaio Ken doubles your speed and power level but its only for an instant and it basically rips your body to shreds the longer you use it. I think the only reason he used it in other world was the same reason why he was able to go SSJ3, his body wasn't really his own.
Think of it as when rock lee opens all the gates, its sorta like that.
If he tried to use Kaio Ken while SSJ in his normal body he would probably die like how vegeta did against buu. Even though he's in SSJ form his body wouldn't be able to contain SSJ boost and Kaio Ken boost at the same time.
If your body isn't built to withhold that much power you'll just explode.
SSJ does more that just raise your power level, it literally transforms your body into being able to withhold and conduct that much power.
That was why frieza thought it was impossible for a saiyan of all creatures to be able to become that powerful that fast.